What does the term "closed expression" mean?
A closed expression refers to a formula which has no free variables [1]. This is also called sentence. In a logic system you have a set of axioms which are sentences and rules which state how to derive a sentence from this [2]. If a sentence can be derived from the axioms, this means that the axioms entail this sentence. If a sentence is not derivable, it is not entailed by the axioms.